Beltrami states for compressible barotropic flows

Beltrami states for compressible barotropic flows are deduced by minimizing the total kinetic energy while keeping the total helicity constant. A Hamiltonian basis for these Beltrami states is sketched. An interesting physical application of the compressible barotropic Beltrami state arises with the Kuzmin-Oseledets formulation of compressible Euler equations. Further, Ertel's invariant is shown to become degenerate in the compressible barotropic Beltrami state.     

Wave Instabilities of a Collisionless Plasma in Fluid Approximation

Wave properties and instabilities in a magnetized, anisotropic, collisionless, rarefied hot plasma in fluid approx‐imation are studied, using the 16‐moments set of the transport equations obtained from the Vlasov equations. These equations differ from the CGL‐MHD fluid model (single fluid equations by Chew, Goldberger, and Low [5,9]) by including two anisotropic heat flux evolution equations, where the fluxes invalidate the double polytropic CGL laws. We derived the general dispersion relation for linear compressible wave modes. Besides the classic incompressible fire hose modes there appear four types of compressible wave modes: two fast and slow mirror modes – strongly modified compared to the CGL model – and two thermal modes. In the presence of initial heat fluxes along the magnetic field the wave properties become different for the waves running forward and backward with respect to the magnetic field. The well known discrepancies between the results of the CGL‐MHD fluid model and the kinetic theory are now removed: i) The mirror slow mode instability criterion is now the same as that in the kinetic theory. ii) Similarly, in kinetic studies there appear two kinds of fire hose instabilities ‐ incompressible and compressible ones. These two instabilities can arise for the same plasma parameters, and the instability of the new compressible oblique fire hose modes can become dominant. The compressible fire hose instability is the result of the resonance coupling of three retrograde modes ‐ two thermal modes and a fast mirror mode. The results can be applied to the theory of solar and stellar coronal and wind models (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

一个新的用于不可压磁流体动力学的格子波尔兹曼模型

绝大多数现有的格子波尔兹曼磁流体动力学模型其实是用可压缩方法来模拟不可压磁流体。而这些可压缩效应在数值模拟中往往会带来意想不到的误差。在这篇文章中，我们提出了一个全新的可用于的不可压格子波尔兹曼磁流体动力学模型，并且进行了哈特曼流的数值模拟。模拟结果与哈特曼流的解析解非常吻合。这个方法需要一个假设条件来消除误差。我们做了大量的数值试验，并且与Dellar教授的模型进行了详细的分析与比较。     

Bilayer coherent and quantum Hall phases: duality and quantum disorder

We consider a fully spin-polarized quantum Hall system with no interlayer tunneling at total filling factor nu = 1/k (where k is an odd integer) using the Chern-Simons-Ginzburg-Landau theory. Exploiting particle-vortex duality and the concept of quantum disordering, we find a large number of possible compressible and incompressible ground states, some of which may have relevance to recent experiments of Spielman et al. [Phys. Rev. Lett. 84, 5808 (2000)]. We find interlayer coherent compressible states without Hall quantization and interlayer incoherent incompressible states with Hall quantization in addition to the usual (k,k,k) Halperin states, which are both interlayer coherent and incompressible.     

Serrin-Type Blowup Criterion for Viscous, Compressible, and Heat Conducting Navier-Stokes and Magnetohydrodynamic Flows

This paper establishes a blowup criterion for the three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic (MHD) flows. It is essentially shown that for the Cauchy problem and the initial-boundary-value one of the three-dimensional compressible MHD flows with initial density allowed to vanish, the strong or smooth solution exists globally if the density is bounded from above and the velocity satisfies Serrin’s condition. Therefore, if the Serrin norm of the velocity remains bounded, it is not possible for other kinds of singularities (such as vacuum states vanishing or vacuum appearing in the non-vacuum region or even milder singularities) to form before the density becomes unbounded. This criterion is analogous to the well-known Serrin’s blowup criterion for the three-dimensional incompressible Navier-Stokes equations, in particular, it is independent of the temperature and magnetic field and is just the same as that of the barotropic compressible Navier-Stokes equations. As a direct application, it is shown that the same result also holds for the strong or smooth solutions to the three-dimensional full compressible Navier-Stokes system describing the motion of a viscous, compressible, and heat conducting fluid.     

Blowup Criterion for Viscous Baratropic Flows with Vacuum States

We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce’s criterion for 3-dimensional incompressible Euler equations (Ponce in Commun Math Phys 98:349–353, 1985). In addition, initial vacuum states are allowed in our cases.     

Theory of four-dimensional fractional quantum Hall states

We propose a pseudo-potential Hamiltonian for the Zhang-Hu’s generalized fractional quantum Hall states to be the exact and unique ground states. Analogously to Laughlin’s quasi-hole (quasi-particle), the excitations in the generalized fractional quantum Hall states are extended objects. They are vortex-like excitations with fractional charges +(−)1/m³ in the total configuration space CP³. The density correlation function of the Zhang-Hu states indicates that they are incompressible liquid.     

Lattice Bhatnagar-Gross-Krook Simulations in 2-D Incompressible Magnetohydrodynamics

Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.     

Lattice Bhatnagar-Gross-Krook Simulations in 2-D Incompressible Magnetohydrodynamics

Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice.Bhatnagar-Gross-Krook （LBGK） model for two-dimensional incompressible magnetohydrodynamics （IMHD） is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.     

无碰撞等离子体电流片中的低频波

采用两种无碰撞二维三分量不可压缩磁流体力学（MHD）模型，计入电子扰动压力张量效应，研究了电流片等离子体的色散性质和波.由于得到的一般色散关系较为复杂，只解析讨论了电流片的中心区和电子β*e=0两种特殊情况.主要结果如下：(1)在短波区（kdi＞1），存在快磁声 动理学Alfven波和斜Alfven 哨声模，电子磁流体力学模型是足够精确的MHD模型；在长波区（kdi＜1＝，存在Alfven波和离子声波，理想的MHD模型是适用的.（2）电子β*e＝0情况下的结果，显然遗漏了一些波模（如离子声波和快磁声动理 关键词： 电流片 磁流体力学 电子压力张量 色散关系     

Hall effect on Hartmann flow and heat transfer of a Burgers' fluid

The effect of Hall current on the steady magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible Burgers' fluid between two parallel electrically insulating infinite planes is studied. The MHD flow is generated by applying constant pressure gradient. An external uniform magnetic field normal to the disks is applied. The disks are kept at two different constant temperatures. Exact solutions are obtained for the governing momentum and energy equations. The effects of Hartmann number M, Reynolds number Re, Prandtl number Pr, Eckert number Ec, pressure gradient dp/dx and Hall parameter η are examined.     

Stable Pfaffian state in bilayer graphene

Here, we show that the incompressible Pfaffian state originally proposed for the 5/2 fractional quantum Hall states in conventional two-dimensional electron systems can actually be found in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. At a finite magnetic field of ~10 T, the Pfaffian state in bilayer graphene becomes more stable than its counterpart in conventional electron systems.     

Compressibility effects on double tearing mode interlocking in differentially rotating plasmas

Effects of compressibility on the double tearing modes (DTMs) in rotating plasmas are numerically investigated by using a compressible magnetohydrodynamics (MHD) model. It is found that due to the compressibility effects, the threshold of the interlocking magnetic island width in the slow and intermediate rotation regimes is larger than the counterpart in the incompressible plasmas. In the fast rotation regime, the compressible effect makes the DTM islands interlock more easily and faster. Moreover, in the very fast rotation regime, the plasma rotation can more effectively suppress the DTM islands. The scalings of the interlocking threshold in the different rotation regimes are obtained. Effects of plasma viscosity and beta on the DTM interlocking in the compressible plasmas are also discussed.     

Low-energy electronic spin excitations between filling factors ν=1 and studied by optically detected nuclear magnetic resonance

We report measurements of the spin relaxation time (T_1n) for nuclei in the potential well confining a high-mobility two-dimensional electron system at a single GaAs–GaAlAs heterojunction. At low temperatures nuclear spin relaxation is dominated by electron–nuclear spin scattering: we find that T_1n displays sharp maxima at incompressible states throughout the hierarchy of the fractional quantum Hall effect. This behaviour is consistent with the existence of low-energy spin excitations only where the electron system is compressible. Our measurements also provide evidence for a gap in the spin excitation spectrum at .     

轴向流对Z箍缩等离子体稳定性的影响

利用理想磁流体力学(MHD)模型对有轴向流参与的Z箍缩等离子体不稳定性进行了分析.对可压缩平板等离子体模型的色散关系进行了推导，讨论了三种不同等离子体状态下的不稳定性增长率.结果显示，等离子体的可压缩性对磁瑞利-泰勒/开尔文-亥姆霍兹(MRT/KH)杂化不稳定性有抑制作用，改善了轴向剪切流对长波长扰动的影响.分析了不同轴向流速度分布对系统稳定性的影响.结果表明，对于峰值相同的不同轴向流，其对不稳定性的抑制效果只依赖于扰动集中区域内速度剪切的大小，与其他位置的速度剪切无关. 关键词： Z箍缩 磁瑞利-泰勒不稳定性 轴向剪切流 MHD方程     

轴向剪切流对Z箍缩等离子体瑞利-泰勒不稳定性的抑制

利用理想磁流体力学模型对有轴向剪切流的Z箍缩等离子体不稳定性进行了分析。给出了可压缩模型的色散关系,分别对可压缩及不可压缩模型中轴向剪切流对Z箍缩等离子体瑞利-泰勒不稳定性的抑制作用进行了比较,讨论了可压缩性对含有轴向剪切流系统不稳定性的影响。结果表明,可压缩性能够减缓瑞利-泰勒P凯尔文-亥姆霍兹(RTPKH)模扰动的增长,因而使得轴向剪切流对系统不稳定性的抑制作用表现得更为突出。计算结果还说明,在RT不稳定性线性增长阶段,等离子体温度较低,使用可压缩模型能够更真实地描述系统的状态。     

Impulse formulations of Hall magnetohydrodynamic equations

Impulse formulations of Hall magnetohydrodynamic (MHD) equations are developed. The Lagrange invariance of a generalized ion magnetic helicity is established for Hall MHD. The physical implications of this Lagrange invariant are discussed. The discussion is then extended to compressible Hall MHD and a generalized ion magnetic potential helicity Lagrange invariant is established. The physical implications of the generalized ion magnetic potential helicity Lagrange invariant are shown to be the same, as to be expected, as those of the generalized ion magnetic helicity Lagrange invariant.     

Nonlinear theory of magnetohydrodynamic flows of a compressible fluid in the shallow water approximation

Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the height of the free boundary on the density of the fluid. Self-similar continuous and discontinuous solutions are obtained for a system on a slope, and a solution is found to the initial discontinuity decay problem in this case.     

Gate-voltage-induced realization of different rational fractions ofh/e2at fixed values of current and magnetic field

We present magnetotransport measurement results obtained on samples with a window-shaped geometry and Schottky gates in the quantum Hall regime. The investigated samples consist of two Hall bars shorted by wide regions of 2DEG. With Schottky gates across each of the Hall bars electron densities and hence filling factors within the two arms of the structures can individually be tuned.We show that by applying appropriate gate voltages to the samples four-terminal resistances equal to different rational fractions ofh/e²can be realized at fixed magnetic field. The measurement results can be explained in the edge channel picture of the quantum Hall effect as well as in a local transport model. In both models it is the interplay between the gate-voltage-induced sub-gate filling factors and the resulting partition of the total current onto the two sample arms that leads to the observed phenomena.     

MHD waves and instabilities in flowing solar flux-tube plasmas in the framework of Hall magnetohydrodynamics

It is well established now that the solar atmosphere, from photosphere to the corona and the solar wind is a highly structured medium. Satellite observations have confirmed the presence of steady flows. Here, we investigate the parallel propagation of magnetohydrodynamic (MHD) surface waves travelling along an ideal incompressible flowing plasma slab surrounded by flowing plasma environment in the framework of the Hall magnetohydrodynamics. The propagation properties of the waves are studied in a reference frame moving with the mass flow outside the slab. In general, flows change the waves’ phase velocities compared to their magnitudes in a static MHD plasma slab and the Hall effect limits the range of waves’ propagation. On the other hand, when the relative Alfvénic Mach number is negative, the flow extends the waves propagation range beyond that limit (owing to the Hall effect) and can cause the triggering of the Kelvin-Helmholtz instability whose onset begins at specific critical wave numbers. It turns out that the interval of Alfvénic Mach numbers for which the surface modes are unstable critically depends on the ratio between mass densities outside and inside the flux tube.